Coherent optical receiver testing

ABSTRACT

An heterodyne apparatus and method for measuring performance parameters of a coherent optical receiver at RF frequencies is disclosed. Two coherent lights are launched into signal and LO ports of the receiver with an optical frequency offset f. One of the lights is modulated in amplitude at a test modulation frequency F. COR performance parameters are determined by comparing two frequency components of the COR output. CMRR is determined based on a strength of a direct detection spectral line at the modulation frequency relative to that of spectrally-shifted lines at (F±f). GDV information is obtained by modulating one of the lights at two phase-locked frequencies, such as F and 2F, and comparing phases of two time-domain traces corresponding to frequency components of the COR output signal at the two frequencies.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/203,939, filed Jul. 7, 2016, now allowed, which is herebyincorporated by reference in its entirety.

FIELD OF THE INVENTION

The invention generally relates to coherent optical receivers, and moreparticularly relates to a method and apparatus for testing andcharacterizing a coherent optical receiver.

BACKGROUND OF THE INVENTION

Coherent optical receivers (COR) are being employed in modernfiber-optic links that utilize coherent optical communication, typicallyin the form of an integrated coherent receiver (ICR) wherein one or moreoptical mixers are tightly integrated with output photodetectors, oftenin a single chip. In order to guarantee a desired level of performanceof a COR in a communication network, the receiver has to be extensivelytested prior to installation with respect to a set of receiverparameters or characteristics. Receiver performance parameters that aretypically measured include the Common Mode Rejection Ratio (CMRR), thegroup delay variation (GDV), the IQ skew, and the polarization skew.

The CMRR, which is an important parameter of coherent optical receivers,determines the capability of a coherent receiver to select onewavelength out of a number of alien wavelengths; the better the CMMR,the more alien wavelengths can be present without distortion of thecommunication signal carried by the target wavelength. Besides that, agood CMRR lowers the RIN (Relative Intensity Noise) requirements for anoptical local oscillator.

The CMRR is a measure how symmetric the internal structures andphotodiode responsivities of a ICR are manufactured, and may be definedas follows:

$\begin{matrix}{{CMRR} = {20\mspace{11mu}{\log_{10}\left( \frac{{I_{1}(f)} - {I_{2}(f)}}{{I_{1}(f)} + {I_{2}(f)}} \right)}}} & (1)\end{matrix}$

where f is a frequency at which the CMRR is measured, and I₁(f) andI₂(f) are the electrical currents from two photodiodes that constitutean output differential detector of the ICR.

A typical ICR may include two input optical paths for two polarizations,which may include two optical mixers such as 90 deg optical hybrids, anddifferential detectors that include pairs of photodiodes followed bytrans-impedance amplifiers (TIA) at the output. Accordingly, CMRR, whichis a combined measure of optical and electrical imbalances in the ICR,may depend on non-idealities along optical paths, e.g. a non-ideal inputoptical splitting ratio (≠3 dB), inaccurate path differences, differingPD responsivities, TIA imbalances, and disbalances in front-endelectronics such as bond wiring and electrical waveguides.

While measuring the CMRR for the continuous wave case, i.e. for f=0, isa relatively easy task, doing that for non-zero frequencies, e.g. in theRF range spanning megahertz (MHz) to tens of gigahertz (GHz) where theICRs typically operate, is not trivial. The photodiodes in the IRC aretypically wired such that only the differential photodiode component isconnected to the output, so that the photodiode currents cannot beaccessed individually, and the sum term in the denominator of equation(1) cannot be accessed directly. Therefore, the CMRR at the RFfrequencies, i.e. RF-CMRR, is difficult to measure.

Another important parameter of a COR is the GDV. The GDV is a measurerelated to time distortion of a signal, and may be determined variationof the group delay of a signal in the COR with frequency. The groupdelay is a measure of the slope of the phase response at any givenfrequency, and is given by the following equation:

$\tau_{g} = \frac{d\;\Phi\;(\omega)}{d\;\omega}$

However, the GDV may also be difficult to measure in integrated photonicdevices based solely on the device output, without access to internalmeasuring points in the device.

Accordingly, it may be understood that there may be significant problemsand shortcomings associated with current solutions and technologies fortesting and characterizing coherent optical receivers, includingintegrated coherent receivers that are used in coherent opticalcommunications.

SUMMARY OF THE INVENTION

Accordingly, an aspect of the present disclosure relates to a method andapparatus for characterizing a coherent optical receiver at one or moremodulation frequencies within an operating frequency range thereof.

An aspect of the present disclosure relates to a method for measuring acharacteristic of a coherent optical receiver (COR) that comprises oneor more optical mixers followed by one or more differentialphotodetectors, the method comprising a) splitting a light from acoherent light source into first and second lights; b) frequencyshifting one of the first or second lights by a frequency shift f; c)modulating the first light in amplitude at a modulation frequency F thatis greater than f; d) providing one of the first and second lights intoa signal port of the COR, and the other of the first and second lightsinto a local oscillator (LO) port of the COR; e) recording an outputsignal of the one or more differential photodetectors from an outputport of the COR, said output signal comprising a first frequencycomponent at a shifted modulation frequency (F−f) or (F+f) and a secondfrequency component; and f) computing the characteristic of the CORbased at least in part on the first and second frequency components. Thesecond frequency component may be, for example, a frequency component ofthe output signal at the modulation frequency F or a shifted harmonic ofthe modulation frequency (n·F−f) or (n·F+f), where n is an integer.

An aspect of the present disclosure provides a method for measuring acharacteristic of a COR that comprises an optical signal port and alocal oscillator (LO) port, the method comprising: a) providing firstcoherent light that is modulated in amplitude at a modulation frequencyF into one of the optical signal port or the LO port of the COR; b)providing second coherent light that is shifted in optical frequencyfrom the first coherent light by a frequency shift f into the other oneof the optical signal port and the LO port of the COR; c) recording oneor more output COR signals from one or more output ports of the COR;and, d) comparing a first frequency component of the one or more outputCOR signals to a second frequency component thereof to determine thecharacteristic of the COR.

An aspect of the present disclosure provides a method for measuring acommon mode rejection ratio (CMRR) of a COR that comprises one or moredifferential photodetectors at the output, the method comprising: a)splitting a light from a coherent light source into first and secondlights; b) frequency shifting one of the first or second lights by afrequency shift f; c) modulating the first light in amplitude at amodulation frequency F that is greater than f; d) providing one of thefirst and second lights into a signal port of the COR, and the other ofthe first and second lights into a local oscillator (LO) port of theCOR; e) recording an output signal of the one or more differentialphotodetectors, said output signal comprising a first frequencycomponent at a shifted modulation frequency (F−f) or (F+f) and a secondfrequency component at the modulation frequency F; determining relativesignal strengths of the first frequency component and the secondfrequency component; and computing the CMRR for the COR based at leastin part on the measured relative strength.

An aspect of the present disclosure provides a method for measuring aCMRR of a COR that comprises an optical signal port, a local oscillator(LO) port, and an output differential detector, the method comprising:a) providing first coherent light that is modulated in amplitude at amodulation frequency F into one of the optical signal port or the LOport of the COR; b) providing second coherent light that is shifted inoptical frequency from the first coherent light by a frequency shift finto the other one of the optical signal port and the LO port of theCOR; c) recording an output signal of the one or more differentialphotodetectors, said output signal comprising a first frequencycomponent at a shifted modulation frequency (F−f) or (F+f) and a secondfrequency component at the modulation frequency F; d) determiningrelative signal strengths of the first frequency component and thesecond frequency component; and e) computing the CMRR of the COR basedat least in part on the first and second frequency components.

An aspect of the present disclosure relates to an apparatus formeasuring a characteristic of a COR. The apparatus comprises one or morecoherent light sources configured to provide first and second lightswith an optical frequency shift f therebetween, and first and secondoutput optical ports for coupling one of the first and second lightsinto a local oscillator (LO) port of the COR and the other of the firstand second lights into an optical signal (OS) port of the COR. Anoptical modulator is disposed in an optical path of the first light andis operable to modulate the first light in amplitude at a modulationfrequency F>f. An electrical signal recorder is further provided that isconfigured to connect to an output port of the COR and to record anoutput COR signal received therefrom, said output COR signal comprisinga first frequency component and a second frequency component. Acontroller is coupled to the electrical signal recorder and isconfigured to determine the characteristic of the COR based at least inpart on the first and second frequency components.

An aspect of the present disclosure relates to an apparatus formeasuring a characteristic of a COR. The apparatus comprises an opticalsplitter for splitting light from a coherent light source into first andsecond lights, and first and second output optical ports for couplingone of the first and second lights into a local oscillator (LO) inputport of the COR and the other of the first and second lights into asignal input port of the COR. An optical modulator is disposed in anoptical path of the first light and is operable to modulate the firstlight in amplitude at a modulation frequency F. An optical frequencyshifter is disposed in an optical path of one of the first and secondlights and is operable to shift an optical frequency of light passingtherethrough by a frequency shift f<F. An electrical signal recorderconfigured to connect to an output port of the COR and to record anoutput signal received therefrom, said output signal comprising a firstfrequency component at a shifted modulation frequency (F−f) or (F+f) anda second frequency component. A controller is coupled to the electricalsignal recorder and configured to determine the characteristic of theCOR based at least in part on the first and second frequency components.The second frequency component may be, for example, a frequencycomponent of the output signal at the modulation frequency F or ashifted harmonic of the modulation frequency (n·F−f) or (n·F+f), where nis an integer.

An aspect of the present disclosure relates to an apparatus formeasuring a CMRR of a COR. The apparatus comprises: an optical splitterfor splitting light from a coherent light source into first and secondlights; first and second output optical ports for coupling one of thefirst and second lights into a local oscillator (LO) input port of theCOR and the other of the first and second lights into a signal inputport of the COR; an optical modulator disposed in an optical path of thefirst light and operable to modulate the first light in amplitude at amodulation frequency F; and an optical frequency shifter disposed in anoptical path of one of the first and second lights and operable to shiftan optical frequency of light passing therethrough by a frequency shiftf<F. An electrical signal recorder is configured to connect to an outputport of the COR and to record an output signal received therefrom, saidoutput signal comprising a first frequency component at a shiftedmodulation frequency (F−f) or (F+f) and a second frequency component atthe modulation frequency F. A controller is coupled to the electricalsignal recorder and configured to determine the CMRR of the COR based atleast in part on a relative strengths of the first and second frequencycomponents in the spectrum of the output signal of the COR.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments disclosed herein will be described in greater detail withreference to the accompanying drawings, which may be not to scale and inwhich like elements are indicated with like reference numerals, andwherein:

FIG. 1 is a schematic block diagram of an apparatus for testing acoherent optical receiver (COR);

FIG. 2 is a flowchart of a method for testing a COR using the apparatusof FIG. 1;

FIG. 3 is a graph of an example measured spectrum of an outputelectrical signal of the COR when tested using the apparatus of FIG. 1with the modulation frequency F of 1 GHz and the optical frequency shiftf=27.12 MHz;

FIG. 4 is a flowchart of an embodiment of the method of FIG. 2 formeasuring the CMRR for the COR;

FIG. 5 is a schematic block diagram of an embodiment of a COR includingtwo optical mixers for polarization diversity and four output channels;

FIG. 6 is a schematic block diagram illustrating an embodiment of theapparatus of FIG. 1 for testing the COR of FIG. 5 in the four outputchannels;

FIG. 7 is a graph illustrating example measured output spectra for afour-channel CMRR measurement;

FIG. 8 is a schematic block diagram illustrating an embodiment of theapparatus of FIG. 6 using a light measuring device to characterize lightprovided to the COR input(s) during measurements;

FIG. 9 is a schematic block diagram of an embodiment of the electricalsignal recorder for use in the apparatus of FIG. 1, 6, or 8;

FIG. 10 is a graph illustrating an example measured output spectrum fora multi frequency test signal;

FIG. 11 is a flowchart illustrating example steps of a method fordetermining the group delay variation (GDV) of a COR;

FIG. 12 is a schematic diagram illustrating MZM modulation with asinusoidal electrical signal for optical harmonic generation;

FIG. 13 is a graph of an example measured spectrum of an outputelectrical signal of the COR when tested using the apparatus of FIG. 1the optical frequency shift f=27.12 MHz and a multi-carrier modulationwith the base modulation frequency F1 of 250 MHz and MZM-generatedsecond harmonic at 500 MHz;

FIG. 14 is a graph illustrating the spectrum of a signal produced bysumming squares of the I and Q outputs of the COR under test;

FIG. 15 is schematic block diagram of an embodiment of an apparatus fortesting a COR using light from two different coherent optical sources tofeed the LO and signal ports of the COR.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, for purposes of explanation and notlimitation, specific details are set forth, such as particular opticalcircuits, circuit components, techniques, etc. in order to provide athorough understanding of the present invention. However, it will beapparent to one skilled in the art that the present invention may bepracticed in other embodiments that depart from these specific details.In other instances, detailed descriptions of well-known methods,devices, and circuits are omitted so as not to obscure the descriptionof the present invention. All statements herein reciting principles,aspects, and embodiments of the invention, as well as specific examplesthereof, are intended to encompass both structural and functionalequivalents thereof. Additionally, it is intended that such equivalentsinclude both currently known equivalents as well as equivalentsdeveloped in the future, i.e., any elements developed that perform thesame function, regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat block diagrams herein can represent conceptual views ofillustrative circuitry embodying the principles of the technology. Thefunctions of the various elements including functional blocks labeled ordescribed as “processors” or “controllers” may be provided through theuse of dedicated hardware as well as hardware capable of executingsoftware in association with appropriate software. When provided by aprocessor, the functions may be provided by a single dedicatedprocessor, by a single shared processor, or by a plurality of individualprocessors, some of which may be shared or distributed. Moreover,explicit use of the term “processor” or “controller” should not beconstrued to refer exclusively to hardware capable of executingsoftware, and may include, without limitation, digital signal processor(DSP) hardware, read only memory (ROM) for storing software, randomaccess memory (RAM), and non-volatile storage.

Furthermore, the following abbreviations and acronyms may be used in thepresent document:

CMRR Common Mode Rejection Ratio

GDV Group Delay Variation

COR Coherent Optical Receiver

ICR Integrated Coherent Receiver

RF Radio Frequency

DSP Digital Signal Processor

FPGA Field Programmable Gate Array

ASIC Application Specific Integrated Circuit

Note that as used herein, the terms “first”, “second” and so forth arenot intended to imply sequential ordering, but rather are intended todistinguish one element from another, unless explicitly stated.Similarly, sequential ordering of method steps does not imply asequential order of their execution, unless explicitly stated. The word‘using’, when used in a description of a method or process performed bya device, component, or circuit, is to be understood as referring to anaction performed by device, component, or circuit itself or by anelement thereof rather than by an external agent. The term ‘analog’refers to signals that encode information in a continuously varyingparameter or parameters, such as for example electrical field, voltage,or current, and to circuits configured to respond to the continuouslyvarying parameter or parameters to process that information; the term‘analog’ may be used herein to distinguish from digital signals orcircuits that encode or process information by switching between afinite set of values or states. In the context of the presentdisclosure, “RF” may refer to frequencies ranging from a few kilohertz(kHz) to tens of gigahertz (GHz).

With reference to FIG. 1, there is schematically illustrated a blockdiagram of an example test apparatus 100 configured for characterizationof a COR 150 under test. The test apparatus 100 may also be referred toherein as the apparatus 100 or as the setup 100. The COR 150 includestwo input optical ports 151 and 152, one of which serves as a signalinput port and the other as an input port for a Local Oscillator (LO).Within COR 150 these optical ports are optically coupled to inputs of anoptical mixer 130, which outputs are coupled to a differential detector140; although only one differential detector is shown, more than onecould be present to detect light from other output ports of the mixer130, if present. The differential detector 140 may be formed of a pairof photodetectors, such as photodiodes (PD), and an output TIA 143. Itwill be appreciated that the optical mixer 130 may include more than twooutput ports, and COR 150 may include more than one optical mixer 130.For certainty in the following description the optical port 152 isassumed to be the LO port of COR 150, and the input optical port 151 isassumed to be the signal port of COR 150.

In the illustrated embodiment, the apparatus 100 includes at its inputan optical splitter 105 for splitting light 103 from a coherent lightsource 101 into first and second lights 106 and 107, which are thendirected along two optical paths 116, 117 to first and second outputoptical ports 111, 112 of the test apparatus 100. The optical paths 116,117 in the apparatus 100 may also be referred to herein as the two armsof the apparatus or the two arms of the setup. The output optical ports111, 112 of the test apparatus 100 are configured to connect to the LOand signal ports of COR 150 so that one of the first and second lightscan be coupled into the LO port 152 of COR 150 and the other of thefirst and second lights—into the optical signal port of COR 150. In theillustrated configuration, the first light 106 is coupled duringmeasurements into the signal port 151 of the COR under test, and thesecond light 107 is coupled into the LO port 152 of COR 150.

An optical frequency shifter (OFS) 109 may be disposed in the opticalpath 116 of the first light 106 to the first output optical port 111 andis operable to shift an optical frequency of light passing therethroughby a frequency shift f. The OFS 109 may be embodied, for example, usingan acousto-optic modulator, which is known in the art to shift theoptical frequency of light it receives by a frequency of an acousticwave generated therein. Other embodiments of the OFS 109 may also beenvisioned, such as for example using an optical modulator followed byan optical filter. In another embodiment the OFS 109 may be disposed inthe optical path 117 to the second output port 112 for couplingfrequency-shifted light into the LO input port 152 of COR 150.

An optical modulator (OM) 110 is operable to modulate light passingtherethrough in intensity at a first modulation frequency F>f andoptionally also at one or more other modulation frequencies in someembodiments, as described hereinbelow. The first modulation frequency Fmay also be referred to herein as the base modulation frequency orsimply as the modulation frequency F. The optical modulator 110 is shownto be disposed in the optical path 116 of the first light 106 after theOFS 109, but in other embodiments may be disposed before the OFS 109 orin the optical path 117 of the second light 107 for coupling into the LOport of COR 150. A variable-frequency electrical signal generator (SG)125 is coupled to the optical modulator 110 for driving it with anelectrical modulation signal at the desired first modulation frequencyF, and in some embodiments at more than one modulation frequencies.

Generally, each of the OM 110 and the OFS 109 may be disposed in anyorder and in any of the two optical paths 116, 117 between the beamsplitter 105 and the output ports 111 and 112 within the apparatus 100.

The coherent light source 101 may be, for example, in the form of asingle-frequency laser that is capable of emitting coherent radiation atan operating wavelength of the COR 150 under test. The coherent lightsource 101 may be, for example a wavelength-stabilized narrow-linewidthsemiconductor laser of a type conventionally used as local oscillatorsfor coherent optical receivers. In some embodiments the coherent lightsource 101 may be included within the apparatus 100. In anotherembodiment, such as that illustrated in FIG. 15, the first and secondlights 106, 107 may be generated by two different coherent light sources171 and 172 that may be frequency-locked to operate at a same opticalfrequency or with a fixed difference fin their optical frequencies, andthe optical splitter 105 may be omitted. In embodiments wherein the twocoherent light sources emit light at optical frequencies that stablydiffer by the desired frequency shift f, the OFS 109 may be omitted, asillustrated in FIG. 15.

The test apparatus 100 may further include an electrical signal recorder160 that is configured to connect to an output port of COR 150 toreceive an output electrical signal 144 from an output COR port 145,which is fed from the differential detector 140. The electrical signalrecorder 160, which may be referred to hereinafter simply as therecorder 160, may include internal circuitry that is configured todetect and/or record the COR output signal 144, and may also beconfigured to extract therefrom desired signal strength or phaseparameters of one or more spectral components of the received signal,for example those that correspond to various linear combinations of thebase modulation frequency F and the optical frequency shift f. Acontroller 170 coupled to the recorder 160 may further be provided forcontrolling various modules of the apparatus 100, and for computing adesired performance characteristics of COR 150 based on the dataextracted by the recorder 160 from the output COR signal 144. Thecontroller 170 may also be configured to extract the desired signalstrength or phase parameters from the signal and/or signals recorded bythe recorder 160. It will be appreciated that the recorder 160 and thecontroller 170 may share a same digital processor for at least some oftheir functions, or may use different digital processors.

Advantageously, apparatus 100 provides a setup for coherent heterodynemeasurement of COR 150 that enables simplified and low noise processingof the COR output signal to obtain data pertinent to a number ofperformance parameters of the COR under test.

Referring now to FIG. 2, there is illustrated a flowchart of a method200 for measuring a performance characteristic of COR 150 using theapparatus 100 according to an embodiment of the present disclosure. Inthe illustrated embodiment, the method starts with a step or operation210 of splitting the light 103 from a coherent light source 101 intofirst and second lights 106, 107 using the optical beam splitter 105. Atstep or operation 220, the first light 106 or the second light 107 isfrequency shifted by the frequency shift f. In embodiments wherein the1^(st) and 2^(nd) light are produced from two different coherent opticalsources and differ in optical frequency by the optical frequency shiftf, steps 210 and 220 may be omitted. At step or operation 230, eitherthe first or the second light is modulated in amplitude at a modulationfrequency F>f using a suitable optical modulator such as the opticalmodulator 110. The operations of the optical frequency shifting andmodulating can be performed in any order, and on either of the first andsecond lights. One of the first and second lights is then provided intoa local oscillator (LO) input port of the COR 150, and the other of thefirst and second lights into the signal port of the COR 150, asindicated at 240. At step or operation 255 the recorder 160 detects and,preferably, records the output signal 144 that is produced by thedifferential detector 140 under test in response to launching the firstand second lights into its input optical ports and appears at the outputport of the COR. The output signal 144 recorded by the recorder 160,which may also be referred to herein as the COR output signal, includesa first frequency component S₁ at a shifted modulation frequency (F−f)or (F+f) and a second frequency component S₂. The second frequencycomponent may be, for example, a component of the output COR signal atthe modulation frequency F or a shifted harmonic of the modulationfrequency (n·F−f) or (n·F+f), where n=1, 2, . . . is an integer. Theterm ‘frequency component’ is used herein to refer to a spectralcomponent of the recorded signal at a specified frequency. In someembodiments the recorder 160 may separately record and compare the firstand second frequency components of the COR output signal 144, which mayinclude spectral components thereof at two of the following frequencies:the modulation frequency F, the shifted modulation frequencies (F±f), asecond harmonic of the modulation frequency 2F, and the shifted secondharmonic (2F±f) of the modulation frequency F. The base modulationfrequency F may be varied during the measurement to obtain the frequencydependence of the COR performance characteristic being measured. At stepor operations 260, one or more performance parameters or characteristicsof the COR 150 under test may be computed by the controller 170 based atleast in part on the first and second frequency components. It will beappreciated that the operations described hereinabove with respect tosteps 255 and 260 may be performed using either the controller 170 orthe recorder 160, depending on a particular implementation of the testapparatus 100.

In one embodiment the apparatus 100 may be configured to implement anembodiment of method 200 to measure a CMRR of a COR under test, such asCOR 150. In this embodiment the second frequency component S₂ refers tothe spectral component of the received COR signal 144 at the basemodulation frequency F, and step 260 may include determining thespectral components of the COR output signal 144 at the base modulationfrequency F and at one or both of the shifted modulation frequenciesF=(F+f) and F=(F−f), and computing the CMRR based at least in part onthe relative signal strength S(F) at the modulation frequency F ascompared to the signal strength S(F^(±)) at at least one of the shiftedmodulation frequencies F⁺=(F+f) and F⁻=(F−f). By way of example, f maybe in the range from a few megahertz (MHz) to several tens of MHz, whilethe base modulation frequency F is typically at least several timesgreater, and may be for example in the range of a few hundred MHz totens of GHz. The base modulation frequency F may be varied by thecontroller 170 across a specified modulation frequency range of the CORunder test, and steps 230-260 repeated for a plurality of values of F inorder to determine CMRR values at a plurality of modulation frequencies.

Principles of the CMRR measurement using the apparatus 100, or asuitably configured embodiment thereof, may be understood by consideringthe relationship between the COR output signal 144 at the recorder 160and the first and second lights 106, 107 at the inputs of the opticalmixer 130 of the COR under test. In the optical mixer 130, the firstlight 106 is coherently mixed with the second light 107. The opticalmixer 130 is conventionally configured so that the photocurrents I₁ andI₂ generated by the PDs 141 are proportional to |E_(sig)+E_(LO)|² and|E_(sig)−E_(LO)|², respectively, and the COR output signal 144, which istaken from the output of the differential detector 140, is typicallyproportional to a difference ΔI between these photocurrents, ΔI=I₁−I₂.Here E_(LO) and P_(LO) denote the optical field and the optical power atthe LO input of the optical mixer 130, and E_(sig) and P_(sig) denotethe optical field and the optical power at the signal input of theoptical mixer 130. In an ideal COR with an ideal differential detector140 at the output, the following relationship holds:ΔI=I ₁ −I ₂∝2Re{E _(sig) ·E* _(LO)}  (2)so that all “direct detection” (DD) terms proportional toP_(sig)(t)=|E_(sig)(t)|² and P_(LO)(t)=|E_(LO)(t)|² in the output CORsignal 144 are eliminated, indicating a perfect common mode rejection.However, internal imbalances in a real-life COR with adifferentially-sources output may result in these DD terms beingpreserved, limiting the CMRR.

Due to the optical frequency shift f in one arm of the setup 100relative to the other arm, COR 150 is operated in the apparatus 100under heterodyne conditions with a fixed intermediate frequency f<F.With an ideal heterodyne differential detection, the coherent beating ofthe signal and LO lights described by the right-hand side of equation(2) results in a spectral line corresponding to the modulation frequencyF being replaced in the output signal of the differential detector 140with two modulation spectral lines at the shifted modulation frequenciesF⁺=(F+f) and F⁻=(F−f). The presence of the common mode signal in the CORoutput may be assessed by the presence of the signal component at themodulation frequency F at the output of the differential detector 140.

FIG. 3 shows by way of example a portion of the spectrum of the outputCOR signal 144 centered about the modulation frequency F for an examplecase of the base modulation frequency F=1 GHz and the optical frequencyoffset f=27.12 MHz. With the heterodyne detection, the spectral linecorresponding to the modulation frequency F=1 GHz is shifted by +/−27.12MHz, resulting in the two shifted modulation spectral lines 41 and 42 atthe shifted modulation frequencies F⁺=(F+f)≈1.027 GHz and F⁻=(F−f)≈0.977GHz; these lines originate from the coherent detecting terms asillustrated by equation (2). The spectral peak 43 at the modulationfrequency F=1 GHz is also visible; this peak stems from the non-coherentdirect detection terms as described hereinabove. The CMRR of a COR beingtested by the apparatus 100 may be determined from the relative signalstrengths of the frequency shifted peaks 41, 42 and the central peak 43if relative optical power of the first and second lights at the input ofthe optical mixer 130 of the COR under test are known. With a perfectCMRR, all photodiodes of the differential receiver of the COR, alloptical and all electrical paths within the COR would have the sameproperties and therefore all direct detection terms would completelycancel out. In an imperfect COR the direct detection terms do not cancelout and the residual spectral peak 43 at the AM modulation frequency Fis visible.

For measuring the CMRR, the optical modulator 110 may be in the form ofany suitable optical intensity modulator that is capable of modulatinglight of a target wavelength with a variable modulation frequency in anoperating frequency range of the COR under test, including but notlimited to an optical absorption modulator and a Mach-Zehnder modulator(MZM). In an example implementation, the optical modulator 110 is an MZMthat is biased at or near a quadrature operating point thereof, i.e., ata voltage where the electro-optical (EO) response T(V) of the modulatoris approximately linear; here V denotes voltage applied to a signalinput of the modulator, and T( ) denotes the optical amplitude or powertransmission coefficient of the modulator, i.e. the ratio of the opticalpower or amplitude at the output of the modulator to that at the input.For measuring the CMRR, the SG 125 may be configured to generate asine-wave electrical signal at the modulation frequency F and to applythat signal to a signal port of the MZM 110. The SG 125 may further beconfigured to vary the modulation frequency F during measurements underthe supervision of the controller 170, with the controller 170cooperating with the recorder 160 to measure the CMRR as a function ofthe modulation frequency at the output of COR 150.

In one embodiment the amplitude V_(mod) of the electrical modulationsignal generated by the SG 125 may be selected to be sufficiently small,e.g., less than Vπ/2, so that the modulating voltage V applied to themodulator stay within the linear portion of the transfer characteristicT(V) in order to avoid the modulation of the light at the output of theMZM 110 to be spread to harmonics nF of the modulation frequency F, suchas 2F. Here, Vπ denotes the modulator voltage that results in a 180°optical phase shift in the MZM arms, as conventionally used in the art.

Under the linear modulation condition, the optical power P_(sig)(t) ofthe first light 106 after the MZM 110 can be approximately described asP _(sig)(t)=

P _(sig)(t)

×[1+m×sin(ω_(mod) t)]  (3)where t represents time, m<1 is the modulation index of the opticalpower at the output of the MZM 110, and ω_(mod)=2πF is the circularmodulation frequency. For m<<1, e.g. m≤⅓, the optical field at theoutput of the MZM may be approximately described by equation (4), whereω_(pt) is the optical frequency of light passing through the MZM:

$\begin{matrix}{{E_{sig}(t)} = {\sqrt{\left\langle {P_{sig}(t)} \right\rangle} \times \left\lbrack {1 + {\frac{m}{2} \times {\sin\left( {\omega_{mod}t} \right)}}} \right\rbrack \times {\cos\left( {\omega_{opt}t} \right)}}} & (4)\end{matrix}$

In the example embodiment of a substantially single-frequencysmall-signal amplitude modulation of the test light 106 or 107 at one ofthe COR optical inputs, the optical power SDD(ω_(mod)) in the ‘directdetection’ spectral line 43 at the modulation frequency F may beestimated asSDD(ω_(mod))=2×CMRR×

P _(sig)(t)

×m,  (5)where ω_(mod)=2πF, and

P_(sig)(t)

≡P_(sig) is the average power of the modulated test light at the CORinput. The optical power S^(coh)(ω_(mod)±ω_(f)) in the spectral lines41, 42 at the shifted modulation frequencies (F±J), ω_(f)=2πf, whichrepresent coherent detection, may be estimated from equation (6):S(ω_(mod)∓ω_(f))=m×√{square root over (

P _(sig)(t)

×

P _(LO)(t)

)}.  (6)We see that the ratio of signal strengths of the respective modulationcomponents given by equations (5) and (6) is proportional to the CMRRbut is independent on the modulation index.

Thus, with a suitably configured apparatus 100 the CMRR may be estimatedfrom comparing the strength of the spectral line at the modulationfrequency F to the strength of the coherent detection lines at theshifted modulation frequencies. In a logarithmic scale, e.g., whenmeasured in decibels (dB), the CMRR value is proportional to thedifference in the total power of the two shifted peaks and the basemodulated peak. Its value is offset by the ratio of the local oscillatorpower and the signal power. Denoting the power of one shifted peak 41 or42 as P_(shift), the power of the base modulation peak 43 as P_(F), thepower of the local oscillator (all values in dB) may be computed asfollows:CMMR_(dB) =A+P _(shift) −P _(F) +P _(sig) −P _(LO),  (7)where ‘A’ denotes a constant that is equal to 6 dB when the modulator110 is a Mach-Zehnder modulator (MZM) biased at the quadrature operatingpoint, but may generally depend on the modulator. The differenceP_(sig)−P_(LO) between optical powers at the signal and LO inputs of COR150 is determined by the difference in optical loss from the input ofthe optical splitter 105 to the output optical ports 111 and 112 of theapparatus, and further to the inputs of the optical mixer 130; it may bedetermined using an optical power meter or an optical spectrum analyzer(OSA) (not shown), or it may be determined by calibration, such as bypre-measuring the power splitting ratio of the optical splitter 105 andthe difference between optical losses in the two optical paths from thebeam splitter to the optical ports 111 and 112. It can be alsodetermined by measuring the DC bias currents of the photodetectors 141of the COR 150.

In one embodiment, the value of the modulation index m may be selectedso as to provide a suitably high signal to noise ratio at the recorder160 while avoiding the appearance of modulation frequency harmonics atthe output of the modulator. By way of example, in one embodiment m maybe selected in the 0.1-0.3 range. The frequency shift f provided by theoptical frequency shifter 109 may be selected to be sufficiently high soas to avoid operating in a regime where the measurement results aredominated by random phase shifts within the measurement setup that mayintroduce a high level of uncertainty in the measured CMRR values, butnot too high, e.g. a few GHz, where the spectral lines at the twoshifted modulation frequencies (F+f) and (F−f) may be affected by S21frequency response variations of the setup, reducing the accuracy of themeasured CMRR. By way of example, an optical frequency shift f may beselected in the range from about 1 MHz to about 100 MHz, or preferablyin the range of about 10 to about 50 MHz, for example 27 MHz.

With reference to FIG. 4, example steps of a method 300 for measuringthe CMRR of a COR using an embodiment of apparatus 100 may be summarizedas follows. Similar to method 200 described hereinabove with referenceto FIG. 2, in the illustrated embodiment the method starts with a stepor operation 310 of splitting the light 103 from a coherent light source101 into first and second lights 106, 107 using the optical beamsplitter 105. At step or operation 320, the first light 106 or thesecond light is frequency shifted by the frequency shift f. At step oroperation 330, the optical power of either the first or the second lightis modulated with a substantially sinusoidal modulation waveform at amodulation frequency F>f, preferably so as to avoid the appearance ofhigher-order harmonics of the modulation frequency in the modulatedlight. In one embodiment, the modulation step may be performed using anMZM that is biased at or near the quadrature operating point and ismodulated with a single-frequency or narrow-band voltage signal withmodulation amplitude less than Vπ/2, so as to ensure the operation in alinear modulation regime. The operations 320 and 330 of the opticalfrequency shifting and modulating can be performed in any order, and oneither of the first and second lights. One of the first and secondlights is then provided into the local oscillator (LO) input port of theCOR 150, and the other of the first and second lights into the signalport of the COR 150, as indicated at 340. At step or operation 350 therecorder 160 may cooperate with the controller 170 to record the outputCOR signal 144 to detect and compare spectral lines S(F) and S(F±f) atone of the shifted modulation frequencies (F−f) or (F+f) and at themodulation frequency F. In some embodiments the recorder 160 or thecontroller 170 may be configured, for example programmed, to compute thespectrum of the recorded COR signal 144. In some embodiments therecorder 160 or the controller 170 may be configured, for exampleprogrammed, to determine the relative strength of the spectral linesS(F) and S(F±f) by first filtering two copies of the recorded output CORsignal with narrow-band filters centered at the shifted modulationfrequencies (F−f) or (F+f) and at the modulation frequency F,respectively, and then determining signal intensities of the twofiltered signals. At step or operations 360, the controller 170 computesthe CMRR for a given modulation frequency F based at least in part onthe strength of the spectral component at the modulation frequency Frelative to that at the shifted modulation frequency (F±f). Themodulation frequency F may be varied during the measurement to obtainthe frequency dependence of the COR performance characteristic beingmeasured.

Although FIG. 1 shows a single differential output channel of COR 150from a single optical mixer 130, in other embodiments, such as thosecommonly used in coherent optical communications, the optical mixer 130may be of the type known as 90° optical hybrid which has four outputports that connect to two differential photodetectors, so as to outputin-phase (I) and quadrature (Q) signals as known in the art.Furthermore, for polarization diversity such a COR may use two opticalhybrids, one for each of two orthogonal polarizations.

Referring now to FIG. 5, there is schematically illustrated a blockdiagram of an embodiment of COR 150 in the form of a dual-polarization,dual-quadrature integrated coherent receiver (ICR) 250. ICR 250 includesa signal optical port 251 that connects to a polarization beam splitter(PBS) 254, which outputs are connected to one of two input ports of eachof two 90° optical hybrids 230. A variable optical attenuator 253 may beconnected between the signal input port 251 and the PBS 254, and amonitoring photodetector 237 coupled at the output thereof to monitorthe optical signal power provided to the optical hybrids 230. An LOinput port 252 connects to a polarization preserving beam splitter (PPS)255, which outputs are connected to the remaining input ports of theoptical hybrids 230. Each of the 90° hybrids 230 have four opticaloutputs that are pair-wise connected to two differential detectors 140.The two 90° hybrids 230 operate at orthogonal optical polarizationcomponents of the input optical signal, and thus provide quadrature Iand Q signals in two polarization channels or planes, which are referredto as X- and Y-(polarization) channels or X- and Y-polarization planesof the COR. Thus, ICR 250 has four output channels providing four outputelectrical signals Ix, Qx, Iy, and Qy that in FIG. 4 are labeled at 144₁ to 144 ₄, respectively. The ICR 250 may be implemented in a singlechip, and may be configured to have a receiver bandwidth of more than 10GHz.

Referring now to FIG. 6, there is illustrated an embodiment of the testapparatus 100, generally indicated at 400, that is configured fortesting multi-channel polarization diversity coherent optical receiversof the type illustrated in FIG. 5. The apparatus 400 includes all of themain components of the apparatus 100, but may additionally include apolarization rotator 115 in the arm of the apparatus that connects tothe signal port 251 of OCR 250. A beam splitter 205 splits light fromthe coherent light source 101 into first and second lights 106, 107 topropagate along two optical paths, or arms, 116 and 117 of theapparatus, which terminate with the first and second output ports 111and 112. The first output port 111 is configured to connect to thesignal port 251 of ICR 250, and the second output optical port 112 isconfigured to connect to the LO port of ICR 250; accordingly, the firstoutput port 111 may also be referred to as the signal output port of theapparatus 400, and the second output port 112 may also be referred to asthe LO output port. The beam splitter 205 may be a polarizationpreserving beam splitter (PPS) that outputs the first and second lights106, 107 of substantially the same polarization. The polarizationrotator 115 may be configured to rotate the polarization of the receivedlight by a desired angle, for example about 45°, so that the lightreceived at the signal port 251 of ICR 250 is split between the twooptical hybrids in desired proportions, and characteristics of the CORmay be measured for orthogonal signal light polarizations. It will beappreciated that the angle of the polarization rotation may differ from45°, for example by as much as +/−15-20°, as long as enough light issent into both optical hybrids of the ICR 250 to allow for asufficiently high SNR at the recorder 160 when signals in bothpolarization planes are measured. Alternatively, the polarizationrotator 115 may be configured to be switchable between a first state inwhich it doesn't change the polarization of the first light 206 and asecond state wherein the polarization at the output of the polarizationrotator 115 is converted to the respective orthogonal polarization.Characteristic of the COR under test for the two orthogonalpolarizations may then be measured, using any of the methods describedherein, in two separate measurement steps in which the polarizationrotator 115 is set to the two different states s. The optical frequencyshifter 107 and the optical modulator 110 in apparatus 400 may bedisposed in either of the two optical paths 116, 117.

The apparatus 400 may operate generally as described hereinabove withreference to apparatus 100 of FIG. 1 and the flowcharts of FIGS. 2 and 4to measure the CMRR in any one of its four output channels Ix, Qx, Iy,and Qy. The recorder 160 in this embodiment may be a single-channeldevice which input connection may be switched between the output portsof the ICR 250. More preferably, the recorder 160 in this embodiment isa four-channel device with four input electrical ports configured toconnect to the four outputs of ICR 250 to simultaneously measure thefour outputs signals 144 ₁-144 ₄ and to determine therefrom the CMRR foreach of the ICR outputs in cooperation with the controller 170. Moreparticularly, in one embodiment the recorder 160 may be configured torecord, sequentially or in parallel, a selected duration of each of thefour output ICR signals 144 ₁-144 ₄, and to determine the strengths oftheir spectral components at the modulation frequency F and the one ormore shifted modulation frequencies (F+f) and (F−f), optionally with thecooperation of the controller 170. The controller 170 may then computethe CMRR for each of the recorded signals by comparing the signalstrength at the base modulation frequency F to that of the shiftedmodulation frequency, as described hereinabove with reference to FIGS.1-4. The computation of the CMRR may take into account the differencebetween the optical powers at the inputs of the ICR 250 as alsodescribed hereinabove, optionally accounting for the settings of the VOA253 and/or any other VOA that may be present in the ICR 250.

FIG. 7 illustrates by way of example four spectra obtained using theapparatus 400 from the four output channels of an example OCR of thetype illustrated in FIG. 5, with the modulation frequency F of 1 GHz andthe optical frequency shift f of 27.12 MHz. The two spectral peaks atthe shifted modulation frequencies 0.97288 GHz and 1.02712 GHz areclearly visible, with the DD peak at the base modulation frequency of 1GHz discernable above the noise level for two of the four channels. TheCMRR values computed for each of the channels using equation (7) areindicated in the figures.

Although in the example embodiments described hereinabove the opticalmodulator 110 is configured to modulate the light intensity at asubstantially single frequency F, in other embodiments the light sent tothe COR under test may be modulated in amplitude at a plurality offrequencies. For example, the optical modulator 110 may operate in anon-linear regime, resulting in the presence of one or more harmonics ofthe modulation frequency F in the AM modulation of the test light thatis sent by the apparatus 100 or 400 into one of the input ports of theCOR. This may happen, for example, for a sufficiently high amplitude ofthe electrical modulation signal at the MZM and/or when the MZM isbiased away from the quadrature point. In another embodiment, themodulator 110 may be modulated with, for example, a square wave whichspectrum includes a plurality of harmonics of the base modulationfrequency. In such embodiments, a number of modulation sub-bands mayappear in the COR output signal, each containing a harmonic nF of themodulation frequency F shifted by ±f, and possibly a direct detectionpeak at the modulation harmonic nF, as illustrated in FIG. 10 showingmultiple modulation subbands centered at multiples of 1 GHz. The CMRRmay be computed in such embodiments for all those sidebands followingthe approach described hereinabove for the single sideband case, takinginto account the distribution of optical power among the sidebands.

Referring to FIG. 8, there is illustrated an embodiment of the apparatus400 that additionally includes a light measuring device (LMD) 221, suchas an OSA or an optical power meter, but may be otherwise substantiallyas described hereinabove with reference to FIGS. 1 and 6. Asillustrated, LMD 221 is optically coupled, for example using opticaltaps, to the two optical paths of the apparatus to measure light provideby the apparatus 400 to the optical inputs of the ICR 250 under test.

In an embodiment wherein the optical spectrum of the first light 206 atthe output of the modulator 110 contains spectral lines at one or moreharmonics of the modulation frequency F, the LMD 221 may be in the formof an OSA that is configured to measure relative strengths of thesespectral lines at the modulation frequency F and its harmonics n·F, n=1,2, 3 . . . , and to communicate this distribution to the controller 170for computing the CMRR values at respective frequencies.

In an embodiment wherein the optical modulation of the first light 206at the output of the modulator 110 contains substantially only themodulation frequency F, the LMD 221 may be an optical power meter thatis configured to measure an optical power ratio P_(sig)/P_(LO) at thesignal and LO inputs of the ICR 250 under test. For example, it mayinclude a single photodetector coupled to an optical switch toseparately test the optical powers at the output ports 111, 112 of theapparatus 400 in cooperation with the controller 170, or it may includetwo photodetectors separately coupled to optical taps disposed in theoptical paths of the first and second lights at the output ports 111,112. The optical powers P_(sig) and P_(LO) measured by the OMD 221 maybe provided to the controller 170, which may be programmed to use themwhen computing the CMRR as described hereinabove, for example withrespect to equation (7). In embodiments of COR 150 or 250 that includesone or more optical components between the signal and LO ports and theoptical mixers, such as for example VOA 253 shown in FIG. 5, theadditional attenuations provided by the VOA(s) and/or other internaloptical components of the COR may be taken into account when computingthe CMRR.

It will be appreciated that the apparatus 100 or 400 may be physicallyimplemented in a variety of ways, including using balk optics and oroptical fibers to embody the optical paths 116 and 117 and to connectvarious optical elements to each other and to the input optical ports ofthe COR under test as illustrated in FIGS. 1, 6, and 8. The electricalsignal recorder 160 may be embodied for example using a high speed realtime oscilloscope, such as a sampling oscilloscope, or an electricalspectrum analyzer. In embodiments configured for testing CORs havingfour output electrical channels for the Ix, Qx, Iy, and Qy signals, asdescribed hereinabove with reference to FIGS. 5, 6, and 8, afour-channel sampling oscilloscope may be used. In embodiments whereinthe recorder 160 is configured to output time-domain traces of thereceived output COR signals 144, the controller 170 may be configured,for example programmed, to perform spectral analysis of those traces todetermine the strength of the spectral component thereof at the basemodulation frequency relative to that at the shifted modulationfrequency or frequencies.

With reference to FIG. 9, in one embodiment the recorder 160 may beimplemented using one or more analog-to-digital converters (ADC) 10 atits input, which is/are operatively followed by a processor 20, which isin turn coupled to a memory device 30. The processor 20 may beimplemented, for example, using a digital signal processor, a suitablehigh-speed microcontroller, an FPGA, or an ASIC. The processor 20 may beconfigured to save sampled time-domain signal or signals received fromthe COR under test in memory 30. The sampling rate of the ADC 10 shouldbe more than twice the modulation frequency F. The duration of the savedsignal may be chosen to be sufficiently large to provide a desiredsignal to noise ratio, for example a few million sampling points.Although implementing the controller 160 using digital logic circuitsand/or processors may be preferable, it will be appreciated that ananalog implementation or a combination of analogue and digital circuitryis also possible and would also be within the confines of the presentdisclosure.

The sampled time-domain trace of the COR output signal 144 may then bepassed to the controller 170 for computing the CMRR. The controller 170may be embodied using a suitable computing device, such as but notexclusively a general purpose digital processor or a suitablemicrocontroller, which may include interfaces for communicating withand/or controlling the SG 125 and optionally other elements of thesetup, such as the OFS 107 and a bias control circuit of the opticalmodulator 110 (not shown in FIGS. 1, 5 and 8). By way of example, thecontroller 170 may be in the form of a computer.

The controller 170 may be programmed to receive the sampled time-domaintraces from the recorder 160, for example by reading the content ofmemory 30, either directly or with the aid of processor 20, and tocompute a spectrum S(o) thereof, where ω represents frequency. Thecontroller 170 may further be programmed to determine, from the computedspectrum, the strength P_(F)=S(2πF) of the direct detection component ofthe spectrum at the base modulation frequency relative to the spectralstrength P_(shift) of the modulation component or components at theshifted modulation frequency, P_(shift)=S(2π(F±f)), and compute the CMRRbased on the determined relative spectral strengths as describedhereinabove.

In one embodiment, the controller 170 may be configured to vary, forexample to increment, the base modulation frequency F across a specifiedfrequency range, for example a frequency range covering the receiverbandwidth of the COR under test, and to determine the CMRR value and/orvalues of other COR performance parameters as described herein for oneor more output channels of the COR for a plurality of values of the basemodulation frequency F that spans the specified modulation frequencyrange.

Advantageously, the general setup of the apparatuses 100 of FIG. 1 orapparatuses 400 of FIGS. 6 and 8 enables measuring not only the CMRR,but other relevant performance parameters of a COR, such as for examplethe phase response Φ(ω) of the COR under test and the group delayvariation (GDV). The GDV is a measure of how the group delay (GD) τ_(g),

$\begin{matrix}{{\tau_{g} = \frac{d\;\Phi\;(\omega)}{d\;\omega}},} & (8)\end{matrix}$that occurs in a device, such as a COR, varies with the RF frequency ωof the received signal.

The phase response Φ(ω), the frequency dependence of the GD τ_(g)(ω),and the GDV of a COR under test may be measured using an embodiment ofthe apparatus 100 or 400 wherein the modulator 110 is configured tomodulate the amplitude, and therefore the intensity and optical power,of the first light 106 simultaneously at the first modulation frequencyF=F₁>f and a second modulation frequency F₂ that is greater than F₁, andthe recorder 160 is configured to simultaneously record time tracesS₁(t) and S₂(t) of two spectral components of the output COR signal 144at the shifted modulation frequencies F₁s=(F₁±f) and F₂s=(F₂±f). Thecontroller 170 may be programmed to compute the GD from a phasedifference ΔΦ between the recorded traces S₁(t) and S₂(t), for exampleby dividing ΔΦ by a frequency difference Δω=2πΔF=2π (F₂−F₁).

With reference to FIG. 11, there is illustrated a flowchart of a method500 for measuring a phase response and the GDV of COR 150 or 250. Themethod 500 may be viewed as an embodiment of method 200 and may beimplemented with the apparatus 100 of 400 that is configured asdescribed hereinabove. In the illustrated embodiment, the method startswith a step or operation 410 of splitting the light 103 from a coherentlight source 101 into first and second lights 106, 107 using the opticalbeam splitter 105. At step or operation 420, the first light 106 or thesecond light is frequency shifted by the frequency shift f. Inembodiments wherein the 1^(st) and 2^(nd) light are produced from twodifferent coherent optical sources and differ in optical frequency bythe optical frequency shift f, steps 210 and 220 may be omitted. At stepor operation 430, either the first or the second light is modulated inamplitude at two phase-locked modulation frequencies, the firstmodulation frequency F=F₁ and a second modulation frequency F₂, whereinF₂>F₁>f, using a suitable optical modulator such as the opticalmodulator 110. The operations of the optical frequency shifting andmodulating can be performed in any order, and on either of the first andsecond lights. One of the first and second lights is then provided intoa local oscillator (LO) input port of the COR 150, and the other of thefirst and second lights into the signal port of the COR 150, asindicated at 440.

The light modulation operation at 430 is performed preferably in aphase-locked manner so that the optical power of the first light 106 atthe output of the modulator 110 is modulated with two sinusoidal signalsat the first and second frequencies F₁=ω₁/2π and F₂=ω₂/2π that may varyin time in proportion to sin(ω₁·t+ϕ₁) and sin(ω₂·t+ϕ₂), respectively,with a phase shift Δϕ=(ϕ₁−ϕ₂) therebetween that does not changesubstantially over a time period of the measurement. The optical signalgenerated at the output of the modulator 110 may be referred to as aphase-locked multi-carrier optical test signal.

At step or operation 450 the recorder 160 detects the output COR signal144 from the differential detector 140 that appears at an output port ofthe COR under test 150 or 250 in response to launching the first andsecond lights into its input optical ports. At this step the recorder160 may sample and record a duration T of the received COR signal, or atleast one or more frequency components thereof. The duration T of therecorded signal S(t) is preferably selected so as to provide a desiredsignal to noise ratio when determining phases of recorded time-domaintraces, for example so as to include many thousands of modulationperiods 1/F₁.

The output COR signal 144 received by the recorder 160 may be filteredto obtain a first time-domain trace S₁(t) corresponding to a firstfrequency component which represents the modulation of the COR signal144 at a shifted first modulation frequency (F₁−f) or (F₁+f), and asecond time-domain trace S₂(t) corresponding to a second frequencycomponent which in this embodiment represents the modulation of the CORsignal 144 at the second shifted modulation frequency (F₂−f) or (F₂+f).The time domain trace S₁(t) may be referred to herein as the first timedomain trace, and the time domain trace S₂(t) may be referred to as thesecond time domain trace. Each of these traces may be obtained, forexample, by applying a suitably narrow-band digital or analog filter tothe recorded COR output signal 144, or to a signal obtain therefrom by apre-processing operation. In one example embodiment, the recorder 160 isa digital signal recorder having at least one ADC 10 followed by thedigital processor 20 at its input as illustrated in FIG. 9, wherein theprocessor 20 may be configured to perform the filtering operations usingdigital filters that may be implemented with software or hardware logicas known in the art. It will be appreciated that tunable analog RFfilters may also be used to select the desired frequency components.

For example, in one embodiment one of the filters may be centered at oneof the first shifted modulation frequencies F₁₁=(F₁−f) or F₁₂=(F₁+f),e.g. F₁₁, and the other filter may be centered at one of the secondshifted modulation frequencies F₂₁=(F₂−f) or F₂₂=(F₂+f), e.g., F₂₁. Inone embodiment, a frequency shifting operation may be applied to eitherthe COR signal 144 received by the recorder 160 or to at least onefrequency component thereof, and one or both of the center frequenciesof the filters may also be correspondingly shifted.

At step or operations 460, the first and second time-domain traces maybe compared to determine a phase difference ΔΦ therebetween. The GDτ_(g) may then be computed, for example by dividing the measured phasedifference ΔΦ by the difference ΔF in the frequencies of the first andsecond time-domain traces. These steps may be performed, for example, bythe controller 170 in cooperation with the recorder 160. The controller170 may be further programmed to vary the first and second modulationfrequencies F₁ and F₂ in a desired wavelength range, for example acrossthe operating frequency band of the COR 150 as may be specified for aparticular COR under test, so as to determine the GD at a plurality offrequencies, and to determine the GDV. In one embodiment, the GDV may besaved and/or presented to a user in the form of a function representingthe measured dependence of the GD on frequency, or as a range (GD_(min),GD_(max)), or in any other suitable form. In one embodiment, the GDV maybe computed as an estimate of the first derivative of the measured GD(F)dependence with respect to the frequency F or 2πF.

The phase-locked multi frequency modulation at step 430 may be performedso that the second frequency F₂ is a harmonic of the first frequency F₁,which may be referred to as the base modulation frequency or simply asthe base frequency. This may include for example modulating themodulator 110 with an electrical modulation signal 128 that includesphased-locked harmonics of the base frequency F₁. The electricalmodulating signal 128 may be for example a periodic signal with period2π/F₁ and a non-sinusoidal waveform, for example a square-wave signal.However, knowledge of the EO phase transfer characteristic of themodulator 110 may then be required at the controller 170 to estimate theGDV.

In a currently more preferred embodiment, the phase-locked multifrequency modulation at step 430 may be performed by applying asubstantially single-frequency electrical modulation signal 128 at thebase frequency F₁ to an embodiment of the modulator 110 that has asubstantially non-linear EO modulation transfer characteristic, so as tocause the optical power of the first light 106 at the output of themodulator 110 to be modulated not only at the base modulating frequencyF₁ but also at one or more harmonics thereof n·F₁, n=2, 3, . . . , usingone of the harmonics as the second modulation frequency F₂. In oneembodiment, the phase-locked multi-frequency modulation operation 430may include using a suitably biased MZM and modulating it with thesinusoidal electrical modulation signal of the base frequency F₁ with anamplitude sufficient to modulate the first light 106 simultaneously atthe first modulating frequency F₁ and the second harmonic thereofF₂=2·F₁. Advantageously, this embodiment does not require any knowledgeof the EO phase transfer characteristic of the modulator 110.

Referring to FIG. 12, a dashed curve 501 schematically shows an exampleEO transfer characteristic T(V) of an MZM 110 as a function of anapplied voltage V. If the MZM is biased at any of the extremes of thetransmission function 501, a small-signal sinusoidal modulation of theMZM at frequency F, i.e., a modulation with an amplitude V<<Vπ/2, wouldresult in a modulation of the output light intensity at the secondharmonic 2F of the modulation frequency F. If the MZM is biased at aquadrature point, i.e. mid-way between two extremes of the transmissionfunction wherein the function T(V) is approximately linear, asmall-signal sinusoidal modulation of the MZM at frequency F wouldresult in a modulation of the output light intensity at the modulationfrequency F. The appearance of both the modulation frequency F₁ and itsharmonic 2F₁ that is phase-locked to the first frequency F₁ in theoptical power of the first light 106 at the output of the MZM 110 may beaffected by modulating the MZM with a sinusoidal voltage signal with anamplitude greater than Vπ/2, and/or biasing the MZM with a suitable biasoffset. An example of such modulation is illustrated in FIG. 12 with acurve 502 representing the sinusoidal modulation signal with a biasoffset 503 from the point of minimum transmission. The resulting opticalintensity of the first light at the output of the modulator isrepresented by the curve 504, where the presence of phase-lockedoscillations at the first modulation frequency F₁ and its harmonic 2·F₁is evident. By way of example, in one embodiment the MZM 110 may bebiased at roughly half the bias voltage corresponding to the quadratureoperating point. In another embodiment, the MZM may be biased closer tothe point of minimum transmission thereby allowing for a smalleramplitude of the voltage modulation, which in that case may be smallerthan Vπ/2, while still resulting in the multi-frequency amplitudemodulation of the output light. Selecting the amplitude of thesinusoidal voltage modulation 502 and the bias voltage offset of the MZM503 so that the first and second harmonics F₁ and F₂ have approximatelyequal power in the optical output of the MZM may be beneficial forachieving a good SNR when determining the relative phases of the twotraces S₁(t) and S₂(t) at step 460, but is not a requirement.

FIG. 13 illustrates by way of example the spectrum of the output CORsignal 144 as may be received by the recorder 160 for the opticalfrequency shift f=27.12 MHz and the base modulation frequency F₁=250MHz. Due to the optical frequency shift in one arm of the setup, the CORunder test is operated under heterodyne conditions with a fixedintermediate frequency f, i.e., 27.12 MHz in this example. Due to theoptical frequency shift in the test apparatus 100 and the heterodynedetection in the COR, the modulated lines at 250 MHz for the basefrequency and at 500 MHz for the second harmonic are shifted each by+/−27.12 MHz resulting in peaks 532 and 533 at (250±27.12) MHz for thefirst shifted modulation components, and peaks 534 and 535 at(500±27.12) MHz for the second shifted modulation components. A line 531at the optical shift frequency f=27.12 MHz is also clearly visible.

Referring back to the flowchart of FIG. 11, it will be appreciated thatthe determination of the phase offset ΔΦ between the first and secondtime-domain traces S₁(t) and S₂(t) may be performed in a variety ofways, all of which would be within the scope of the present disclosure.For example, it may include determining relative timings of the minimaor zeros in the recorded traces. A complication with this approach isthat neither of the two second shifted frequencies F_(2±)=(F₂±f) is aharmonic of one of the two first shifted modulation frequenciesF_(1±)=(F₁±f) even when the second modulation frequency is a harmonic ofthe first modulation frequency, i.e., F₂=2F₁. Accordingly, in oneembodiment step 450 may include shifting one of the recorded COR signalS(t), the first time-domain trace S₁(t), and the second time-domaintrace S₂(t) in frequency so that, after this frequency shiftingoperation, the second trace becomes a harmonic of the first trace. Forexample, the recorded COR signal S(t) may be shifted in frequency by thefrequency shift equal in value to the optical frequency shift f imposedby the optical shifter 109. This frequency shift operation may beperformed, for example, in a digital domain by computingS _(shift)(t)=exp(i2πft)S(t)

This operation transforms one of the first shifted modulationfrequencies (F₁±f) back to the first modulation frequency F₁, and one ofthe two shifted second modulation frequencies (2F₁±f) to its secondharmonic F₂=2F₁. Next, two band-pass filters with linear group delaycentered at the first modulation frequency F₁ and its harmonic 2F₁,respectively, such as for example Gaussian filters, may be applied tothe shifted received signal S_(shift)(t) to obtain the first and secondtime-domain traces S₁(t) and S₂(t), which are now in the form ofsinusoidal oscillations at the modulation frequency F₁ and its harmonic2F₁. The relative phase between these two tine-domain traces may then bedetermined using any suitable method, as will become apparent to thoseskilled in the art.

In one example embodiment the phase offset ΔΦ between the first andsecond time-domain traces may be determined by evaluating the timebetween the zero crossings of the two sine waves representing the tracesS₁(t) and S₂(t). For example, the controller 170 may be programmed todetect the time difference between the positive slope zero crossings ofthe trace S₁(t) at the base modulation frequency F₁ and the positiveslope zero crossings of S₂(t) at the first harmonic of the basefrequency F₁. The relative phase ΔΦ may then be computed from the knownbase frequency F₁. In order to get a good SNR (signal to noise ratio),the comparison may be performed for thousands of zero crossings, andpreferably over a longer signal, for example including hundreds ofthousands of the base modulation periods.

Further by way of example, ΔΦ may be also determined by squaring thefirst time-domain trace S₁(t), i.e., performing the operation S₁(t)→S₁²(t), thus doubling its frequency, and then shifting the squared traceS₁ ²(t) against the second harmonic trace S²(t) while computing theirscorrelation function until the best correlation is reached.

In another example, ΔΦ may be also determined by first passing bothtraces S₁ and S₂ through a logical circuit, or a software routine,implementing the signum function. The output of the signum function is asquare wave switching between plus one and minus one, depending of thesign of the respective trace. Applying the XOR operation to the twooutputs of the signum function and calculating the mean value of theresult gives information about the relative phase ΔΦ between the firstand second time domain traces. Those skilled in the art will be able todevise other ways to determine the relative phase of the two harmonicwaves S₁ and S₂ having the benefit of the present description.

Thus in one embodiment method 500 may include modulating a suitablybiased MZM with a sinusoidal electrical modulating signal of a basefrequency F₁ so as to affect an intensity modulation of the first testlight 106 at the base frequency F₁ and the second harmonic thereof 2F₁,and determining the GD of the COR under test from the output COR signalby comparing two time-domain traces thereof as described hereinabove.These operations may be repeated for a plurality of base frequencyvalues to obtain information about the GDV.

The value of the optical frequency shift f for measuring the GDV may bedetermined from considerations similar to those described hereinabove inrelation to measuring the CMRR; furthermore, it may be preferred toselect f so that the GDV over the frequency span of width f isrelatively small. By way of example, it may be in the range from a fewMHz to tens of MHz, for example in the 10-50 MHz range. In embodimentswherein a second laser is used to produce the frequency-shifted light,the phase noise of the two lasers may result to inaccuracies in GDVmeasurements; using frequency-stabilized lasers with spectral linewidthmuch smaller than f may facilitate more accurate GDV measurements.

In embodiments wherein the COR under test has multiple output channels,such as the ICR 250 described hereinabove with reference to FIG. 5,method 500 may be applied to each of the output channel of the COR undertest, for example using an embodiment of the apparatus 400 illustratedin FIG. 6 or 8 wherein the recorder 160 and the controller 170 areconfigured to perform steps 450 and 460 of the method describedhereinabove with reference to FIG. 11. By using thepolarization-maintaining beam splitter 205 in combination with thepolarization rotator 115, both polarization planes of the ICR 250receive a signal and can be sampled simultaneously using a suitablyconfigured recorder 160. For example, the recorder 160 may be configuredto have four input channels for receiving the four COR signals 144 ₁-144₄, and to independently process each of these signals, eithersequentially in time or in parallel, as described hereinabove withrespect to the output COR signal 144, to obtain GDV information for thefour output COR channels Ix, Qx, Iy, and Qy. In another embodiment, anRF signal switch (not shown) may be used in front of the recorder 160 tosequentially test the output channels of the ICR 250.

The apparatus 400 of FIG. 6 or 8 with the recorder 160 having four inputchannels may also be configured to determine an IQ skew parameter andpolarization skew parameter of the COR under test. The IQ skew relatesto a phase offset between the I and Q COR output signals of the samepolarization plane, i.e., a phase offset ΔΦ_(IQx) between the Ix outputsignal 144 ₁ and the Qx output signal 144 ₂, or a phase offset ΔΦ_(IQy)between the Iy output signal 144 ₃ and the Qy output signal 144 ₄. Thesephase offsets may be determined by configuring the recorder 160 and/orthe controller 170 to simultaneously record the I and Q signals of thesame polarization plane from the COR under test, to filter the recordedsignals to obtain time-domain traces S_(I)(t) and S_(Q)(t) of a samefrequency component F_(w) thereof, and to compare these traces todetermine a relative phase shift therebetween ΔΦ_(IQ). The frequencycomponent F_(w) may correspond to any one of the four shifted modulationfrequencies (F₁±f) and (F₂±f) corresponding to peaks 532-535 in FIG. 13.

By design, oscillations at any intermediate frequency in the ‘I’ and ‘Q’output quadrature signals in each polarization plane of a COR shouldhave a relative phase shift of 90°; here the intermediate frequency isunderstood as one of the frequency components in the I and Q outputquadrature signals 144 i, including the optical frequency shift fin oneof the arms of the apparatus 100 or 400, or the shifted modulationfrequencies (F±f). However, this phase shift in a non-ideal COR mayslightly differ from 90°, indicating an internal I-Q phase disbalance inthe COR and a skew, i.e. a time delay, in the signal travel time for theI or the Q signal, such as for example due to different cable lengths.In one embodiment the controller 170 and/or the recorder 160 may beconfigured to implement a method to determine the I-Q phase disbalanceand the IQ skew in a COR under test by performing the followingoperations. First, the IQ phase shift ΔΦ_(IQ) may be measured for aplurality of different modulation frequencies F. The measured dependenceΔΦ_(IQ)(F) may then be linearly extrapolated to a zero modulationfrequency F, i.e. to F=0. The resulting extrapolated value ΔΦ_(IQ)(0)may be provided to the user as an estimate of the internal I-Q phaseshift of the COR, which should be equal to 90° in an ideal COR. Itsdeviation from the nominal value of 90° may be provided as an estimateof the I-Q disbalance of the COR under test. A slope of the measureddependence ΔΦ_(IQ)(F) of the IQ phase shift versus the modulationfrequency F, i.e., d[ΔΦ_(IQ)(F)]/dF, provides information about the IQskew and may also be computed by the controller 170 and/or the recorder160 based on the measured dependence ΔΦ_(IQ)(F) of the IQ phase shiftbetween the output I and Q signals of the COR under test on themodulation frequency F.

Due to the nominally 90° phase shift between the intermediate-frequencyoscillations in the I and Q signals at the output of the COR under test,the oscillations at the intermediate frequency f should cancel out whenthe total signal power P_(Z)(t)=I_(Z) ²(t)+Q_(Z) ²(t) in both the I andQ channels is measured. Here, the subscript ‘Z’ stands for either of thepolarization plane indices ‘X’ or ‘Y’ to indicate output signals ineither of the two polarization planes ‘X’ and ‘Y’ of the COR under test.Indeed, if the ‘I’-channel output from the COR is proportional to a sineof the intermediate frequency f, i.e., sin(2πf), the ‘Q’-channel outputfrom the same optical mixer in the COR, i.e., of the same polarizationplane, should be proportional to the cosine of the intermediatefrequency f, i.e., cos (2πf). Since sin²(a)+cos²(a)=1, the spectralcomponents in the output power signal P_(Z)(t) at the intermediatefrequency f and the shifted modulation frequencies (F±f) should cancelout, while the amplitude modulation at the modulation frequency F isrestored.

In one embodiment the recorder 160 or controller 170 may be configuredto determine the polarization skew of the COR under test 250 bycomparing time-domain traces of the recovered amplitude modulation ofthe output power signals P_(X) and P_(Y) at the base modulationfrequency F in the two polarization planes. In one embodiment, in orderto determine the polarization skew of the COR under test, the recorder160 and/or the controller 170 may be configured to simultaneously recordthe Ix, Qx, Iy, and Qy signals 144 ₁, 144 ₂, 144 ₃ and 144 ₄ of the twopolarization planes from the COR under test, to compute amplitudemodulated signals A_(X)(t) and A_(Y)(t) representative of total outputpower of both I and Q signals for each polarization plane as function oftime t, and to determine a relative phase ΔΦ_(XY)(F) between time-domaintraces of frequency components of the respective amplitude modulatedsignals at the modulation frequency F. This process may include: a)summing the squares of I and Q output signals separately for each of theX and Y polarization planes of the COR under test to obtain theamplitude modulated signals A_(X)(t) and A_(Y)(t) of the twopolarization planes as functions of time, as described by the followingequations:Δ_(X)(t)=(Ix)²+(Qx)²andA _(Y)(t)=(Iy)²+(Qy)²

b) filtering these power signals with a suitably narrow pass-band filterto obtain time-domain traces S_(X)(t) and S_(Y)(t) of their frequencycomponents at the modulation frequency F, and

c) comparing these traces to determine a relative time shift Δτ_(XY)between the time domain traces of the power modulation components of thetwo polarization planes of the COR.

The above-described exemplary embodiments are intended to beillustrative in all respects, rather than restrictive, of the presentinvention. Indeed, various other embodiments and modifications to thepresent disclosure, in addition to those described herein, will beapparent to those of ordinary skill in the art from the foregoingdescription and accompanying drawings. Thus, such other embodiments andmodifications are intended to fall within the scope of the presentdisclosure. For example, FIG. 15 illustrates an embodiment of the testapparatus of FIG. 1 wherein, instead of splitting the light from onecoherent optical source into the first and second lights and frequencyshifting one of the lights, two very stable and spectrally closelyspaced independent lasers 171 and 172 may be used; the lasers may befrequency locked, or may emit at optical frequencies that differ by theoptical shift f, and have narrow spectral linewidth that are less thanf. It will be appreciated that two such lasers may also be used in otherembodiments of the test apparatus of the present disclosure, such as forexample those illustrated in FIGS. 6 and 8.

Although the theoretical description given herein is thought to becorrect, the operation of the devices described and claimed herein doesnot depend upon the accuracy or validity of the theoretical description.That is, later theoretical developments that may explain the observedresults on a basis different from the theory presented herein will notdetract from the inventions described herein.

While the present invention has been particularly shown and describedwith reference to the preferred mode as illustrated in the drawing, itwill be understood by one skilled in the art that various changes indetail may be affected therein without departing from the spirit andscope of the invention as defined by the claims.

What is claimed is:
 1. An apparatus for measuring a characteristic of acoherent optical receiver (COR) that comprises one or more opticalmixers followed by one or more differential photodetectors, theapparatus comprising: one or more coherent light sources configured toprovide first and second lights with an optical frequency shift ftherebetween, wherein the first light is modulated in amplitude at afirst modulation frequency F₁>f, and, first and second output opticalports for coupling one of the first and second lights into a localoscillator (LO) port of the COR and the other of the first and secondlights into an optical signal port of the COR.
 2. The apparatus of claim1 wherein the one or more coherent light sources comprises a firstcoherent light source and a second coherent light source wherein thefirst and second coherent light sources are configured to emit lightwith the frequency shift f therebetween.
 3. The apparatus of claim 2wherein the first coherent light source and the second coherent lightsource are frequency-locked to operate with the frequency shift ftherebetween.
 4. An apparatus for measuring a characteristic of acoherent optical receiver (COR) that comprises one or more opticalmixers followed by one or more differential photodetectors, theapparatus comprising: one or more coherent light sources configured toprovide first and second lights with an optical frequency shift ftherebetween, wherein the first light is modulated in amplitude at afirst modulation frequency F₁>f, first and second output optical portsfor coupling one of the first and second lights into a local oscillator(LO) port of the COR and the other of the first and second lights intoan optical signal port of the COR; a signal recorder configured toconnect to an output port of the COR and to record an output COR signalreceived therefrom, said output COR signal comprising a first frequencycomponent and a second frequency component; and, a controller coupled tothe electrical signal recorder and configured to determine thecharacteristic of the COR based at least in part on the first and secondfrequency components.
 5. The apparatus of claim 4 wherein the one ormore coherent light sources comprise a first coherent light source, abeam splitter disposed for splitting light from the first coherent lightsource into the first and second light beams, and an optical modulatordisposed in an optical path of the first light and operable to modulatethe first light in amplitude at the first modulation frequency F₁. 6.The apparatus of claim 5 including an optical frequency shifter disposedin an optical path of one of the first and second lights and operable toshift an optical frequency of light passing therethrough by the opticalfrequency shift f.
 7. The apparatus of claim 6 wherein the opticalfrequency shifter comprises an acousto-optic modulator.
 8. The apparatusof claim 5 wherein the optical modulator comprises a Mach-Zehndermodulator (MZM).
 9. The apparatus of claim 5 further comprising apolarization rotator disposed in an optical path of one of the first andsecond lights to the signal optical port of the COR.
 10. The apparatusof claim 5 further comprising a frequency-variable electrical signalgenerator coupled to the optical modulator and configured to generate anelectrical modulation signal at the first modulation frequency F₁,wherein the controller is coupled to the frequency-variable electricalsignal generator and is configured to vary the first modulationfrequency F₁ and to compute the characteristic of the COR at a pluralityof values of the first modulation frequency F₁.
 11. The apparatus ofclaim 10 configured for measuring a common mode rejection ratio (CMRR)of the COR, wherein the electrical signal recorder is configured torecord a time-domain trace of the received signal, and wherein thecontroller is configured to process said trace to determine therefrom arelative signal strength of the first frequency component measured atthe shifted modulation frequency (F₁−f) or (F₁+f) relative to the secondfrequency component measured at the first modulation frequency F, and tocompute the CMRR based at least in part on the relative signal strengthof the first and second frequency components.
 12. The apparatus of claim11 wherein the optical modulator comprises a Mach-Zehnder modulator(MZM) that is configured to be biased at or near a quadrature point, andwherein the electrical signal generator is configured to generate theelectrical modulating signal in the form of a voltage sine wave at thefirst modulation frequency F₁ with an amplitude that is less than halfof a characteristic Vπ voltage of the MZM.
 13. The apparatus of claim11, further comprising an optical power meter disposed to measureoptical power of the first and second light at the output optical ports,wherein the controller is coupled to the optical power meter andconfigured to compute the CMRR based in part on the measured opticalpower of the first and second lights.
 14. The apparatus of claim 11including an optical spectrum analyzer disposed to measure opticalspectrum of the first light after the optical modulator at one or moreharmonics of the first modulation frequency F₁.
 15. The apparatus ofclaim 4 wherein the first light is modulated also at a second modulationfrequency F₂>F₁, and wherein the controller is configured to obtain,from a duration of the output COR signal recorded by the recorder, afirst time-domain trace corresponding to a frequency component of theoutput COR signal at a first shifted modulation frequency (F₁+f) or(F₁−f) and a second time-domain trace corresponding to a frequencycomponent of the output COR signal at a second shifted modulationfrequency (F₂+f) or (F₂−f), to determine a phase shift between the firstand second time-domain trances, and to compute a group delay variation(GDV) for the COR based on the phase shift.
 16. The apparatus of claim15 comprising an optical modulator disposed in an optical path of thefirst light and operable to modulate the first light in amplitude at thefirst modulation frequency F₁ and the second modulation frequency F₂ inin a phase-locked manner.
 17. The apparatus of claim 16 wherein theoptical modulator has a non-liner electro-optical modulation transfercharacteristic, comprising an electrical signal generator that iscoupled to the optical modulator and is configured to generate theelectrical modulating signal at the first modulation frequency F₁, theelectrical modulating signal characterized by a substantially sinusoidalwaveform of an amplitude sufficient to modulate an optical power of thefirst light at the first modulation frequency F₁ and the secondmodulation frequency F₂=2F₁.
 18. The apparatus of claim 17 wherein thecontroller is coupled to the electrical signal generator and isconfigured to vary the first modulation frequency F₁, to obtain a phaseresponse of the COR as a function of frequency, and to compute the GDVfor a plurality of frequencies based on the phase response.
 19. Theapparatus of claim 4 wherein the COR comprises two output portsconfigured to output in-phase (I) and quadrature (Q) signals, whereinthe signal recorder is configured to connect to each of the two outputports of the COR and to record each of the I and Q signals, and whereinthe controller is configured to: a) apply a pass-band filter to one ofthe I and Q signals at a shifted modulation frequency (F+f) or (F−f) toobtain the first frequency component; b) apply a pass-band filter to theother one of the I and Q signals at the shifted modulation frequency toobtain the second frequency component; c) determine an IQ phasedifference ΔΦ_(IQ) between the first frequency component and the secondfrequency component; d) repeat steps (a) to (c) for a plurality ofmodulation frequencies F to obtain the IQ phase difference ΔΦ_(IQ) as afunction of frequency ΔΦ_(IQ)(F); and, e) estimate at least one of: anIQ skew based on a slope of the IQ phase difference ΔΦ_(IQ)(F) as afunction of frequency, and an I-Q phase disbalance in the COR based onan extrapolation of the the IQ phase difference ΔΦ_(IQ)(F) to zerofrequency.
 20. An apparatus of claim 4 wherein the COR comprises fouroutput ports configured to output in-phase (Ix) and quadrature (Qx)signals of a first polarization, and in-phase (Iy) and quadrature (Qy)signals of a second polarization, wherein the signal recorder isconfigured to connect to each of the four output ports of the COR torecord the Ix signal, the Iy signal, the Qx signal, and the Qy signal,and wherein the controller is configured to: a) sum squares of the Ixand Qx signals to obtain a power signal Ax of the first polarizationplane ‘X’ of the COR; b) sum squares of the Iy and Qy signals to obtaina power signal Ay of the second polarization plane ‘Y’ of the COR; and,c) estimate a time delay Δτ_(XY) between frequency components of thepower signals Ay and Ax at the modulation frequency F to determine apolarization skew of the COR.